Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

Develops and tests a function-based approach to algebra called the Visual Mathematics curriculum in grades 7-9. Presents a theoretical framework for a systemic investigation of the structures of algebra word problems and their relationship to function-based solutions. Suggests new insights into categorizing word problems. (Contains 19 references.)…

Presents a device for sketching the graph of the composite and inverse of single variable real-valued functions. Discusses some didactic methods of paths. (YP)

Develops a method for visualizing the complex roots of a polynomial equation. Illustrates some quadratic or cubic polynomials and their solutions. (KHR)

Describes two thought experiments, involving visualizing the behavior of functions, that can be turned into computer experiments. (MKR)

This two volume collection of proceedings contains working group reports, research reports, oral reports, poster session reports and discussion group reports presented at PME-NA 21. Only the plenary and research reports are full reports; the others are brief abstracts. Full reports include: (1) "Representation, Vision and Visualization:…

Introduces an introductory module for analysis. Describes stock of basic functions and their graphs as part one and three methods as part two: transformations of simple graphs, the sum of stock functions, and upper and lower bounds. (YP)

Discusses a technique for graphically composing functions. Describes three-step composition procedures in two- and three-dimensional rectangular coordinate systems. Provides three examples. (YP)

Few would argue that students struggle with understanding and representing functions. There are many theories on why the abstraction of mathematical processes poses such cognitive difficulty, but so far functional programming is most often taught in a manner that discourages the use of visual intuition. The paper, by contrast, describes a…

Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…

Presents activities that utilize representations of the side, front, and top views of three-dimensional configurations of blocks to develop spatial-visualization skills and aspects of the concept of function. Provides worksheets of these open-ended investigations. (MDH)

This paper considers how the algebra curriculum in secondary mathematics might be reformulated by rethinking both the content of algebra and the approaches to teaching and learning algebraic concepts. It considers how the concept of function can be made a central theme of the algebra curriculum and further suggests that computer software, when…

Suggests that intuition and visualization are effective methods of introducing engineering principles to pre-engineering students. Describes the development of computer simulation software as part of a "Pre-Engineering College On Disk" course. The computer game helps students visualize the relationship between shell trajectory and its…

The purpose of a seminar attended by mathematics educators from the United States and Japan was to explore ways that use of technology in teaching problem solving can improve student learning. The following presentations were made: (1) "A Report of U.S.-Japan Cross-cultural Research on Students' Problem-Solving Behavior," (T. Miwa and T.…